A stochastic SIS epidemic with demography: initial stages and time to extinction

Journal of Mathematical Biology
Patrik Andersson, David Lindenstrand


We study an open population stochastic epidemic model from the time of introduction of the disease, through a possible outbreak and to extinction. The model describes an SIS (susceptible-infective-susceptible) epidemic where all individuals, including infectious ones, reproduce at a given rate. An approximate expression for the outbreak probability is derived using a coupling argument. Further, we analyse the behaviour of the model close to quasi-stationarity, and the time to disease extinction, with the aid of a diffusion approximation. In this situation the number of susceptibles and infectives behaves as an Ornstein-Uhlenbeck process, centred around the stationary point, for an exponentially distributed time before going extinct.


Jun 6, 2002·Mathematical Biosciences·Ingemar Nåsell

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